Water vapor flux

Fuel cell operation entails (1) coupled proton migration and water fluxes in the PEM, (2) circulation and electrochemical conversion of electrons, protons, reactant gases, and water in CLs, and (3) gaseous diffusion and water exchange via vaporization/condensation in pores and channels of CLs, GDLs, and EEs. All components of an operating cell have to cooperate well in order to optimize the highly nonlinear interplay of these processes. It can be estimated that this optimization involves several 10s of parameters. 

Chemical equilibrium corresponds to zero water flux and uniform chemical potential of water in the membrane interior and in the external vapor phase. 

Continuity of fhe wafer flux fhrough the membrane and across the external membrane interfaces determines gradients in water activity or concentration these depend on rates of water transport through the membrane by diffusion, hydraulic permeation, and electro-osmofic drag, as well as on the rates of interfacial kinetic processes (i.e., vaporization and condensafion). This applies to membrane operation in a working fuel cell as well as to ex situ membrane measuremenfs wifh controlled water fluxes fhat are conducted in order to study transport properties of membranes. 

This condition has been recently used in a vaporization-exchange model for water sorption and flux in phase-separated ionomer membranes. The model allows determining interfacial water exchange rates and water permeabilities from measurements involving membranes in contact with flowing gases. It affords a definition of an effective resistance to water flux through the membrane that is proportional to... 

Weber and Newman do the averaging by using a capillary framework. They assume that the two transport modes (diffusive for a vapor-equilibrated membrane and hydraulic for a liquid-equilibrated one) are assumed to occur in parallel and are switched between in a continuous fashion using the fraction of channels that are expanded by the liquid water. Their model is macroscopic but takes into account microscopic effects such as the channel-size distribution and the surface energy of the pores. Furthermore, they showed excellent agreement with experimental data from various sources and different operating conditions for values of the net water flux per proton flux through the membrane. 

H. Gieseler, W.J. Kessler, M. Finson, et al.. Evaluation of tunable diode laser absorption spectroscopy for in-process water vapor mass flux measurements during freeze drying, J. Pharm. Sci., 96(7), 1776-1793 (2007). 

To avoid cathode flooding, a hydrophobic cathode backing and an efficient means to remove water droplets in the cathode flow field are required. We report here measurements of water flux in both liquid and vapor forms in the cathode... 

Figure 17 displays the T-compensated HFR as a function of the through-plane vapor diffusion flux. If there is sufficiently large flow rate, the resulting HFR should no longer be affected by the convective flux of water vapor down the channel, and hence the HFR would... 

Equation (2.79) expresses the driving force in pervaporation in terms of the vapor pressure. The driving force could equally well have been expressed in terms of concentration differences, as in Equation (2.83). However, in practice, the vapor pressure expression provides much more useful results and clearly shows the connection between pervaporation and gas separation, Equation (2.60). Also, the gas phase coefficient, is much less dependent on temperature than P L. The reliability of Equation (2.79) has been amply demonstrated experimentally [17,18], Figure 2.13, for example, shows data for the pervaporation of water as a function of permeate pressure. As the permeate pressure (p,e) increases, the water flux falls, reaching zero flux when the permeate pressure is equal to the feed-liquid vapor pressure (pIsal) at the temperature of the experiment. The straight lines in Figure 2.13 indicate that the permeability coefficient d f ) of water in silicone rubber is constant, as expected in this and similar systems in which the membrane material is a rubbery polymer and the permeant swells the polymer only moderately. 

Figure 2.13 The effect of permeate pressure on the water flux through a silicone rubber pervaporation membrane. The arrows on the lower axis represent the saturation vapor pressures of the feed solution at the temperature of these experiments as predicted by Equation (2.79) [15]...

Figure 13.14 Water flux across a microporous membrane as a function of temperature and vapor pressure difference (distillate temperature, 18-38 °C feed solution temperature, 50-90 °C). Taken from the data of Schneider el al. [31]...

Generally, 70 to 75% of the water vaporized on land is transpired by plants. This water comes from the soil (soil also affects the C02 fluxes for vegetation). Therefore, after we consider gas fluxes within a plant community, we will examine some of the hydraulic properties of soil. For instance, water in the soil is removed from larger pores before from smaller ones. This removal decreases the soil conductivity for subsequent water movement, and a greater drop in water potential from the bulk soil up to a root is therefore necessary for a particular water flux density. 

This volumetric water flux density directed upward at the soil surface equals (1 x 10-8 m3 m-2 s 1)(l mol/18 x 10-6 m3), or 0.6 x 10-3 mol mT s-1 (= 0.6 mmol m-2 s-1). When discussing water vapor movement in the previous section, we indicated that Jm> emanating from a moist shaded soil is usually 0.2 to 1.0 mmol m-2 s-1, so our calculated flux density is consistent with the range of measured values. The calculation also indicates that a fairly large gradient in hydrostatic pressure can exist near the soil surface. 

In SGMD, a hot feed solution is circulated on one side of a microporous membrane and cold sweep gas on the other side of the membrane. The temperature difference gives rise to a water vapor pressure difference, and consequently, to a water flux through the membrane. 

Equation (3) establishes a relationship between controlled water vapor pressure P, capillary pressure Pc and pore radius r. Equation (2) relates Pc to the external gas pressure Pg and the internal liquid pressure P1, whose gradient is the driving force of water flux. The presented formalism, thus, provides a closed set of equations that relate the stationary water profiles in the membrane with its porous structure. 

The role of the porous structure and partial liquid-water saturation in the catalyst layer in performance and fuel cell water balance has been studied in Ref. 241. As demonstrated, the cathode catalyst layer fulfills key functions in vaporizing liquid water and in directing liquid-water fluxes in the cell toward the membrane and cathode outlet. At relevant current densities, the accumulation of water in the cathode catalyst layer could lead to the failure of the complete cell. The porous structure controls these functions. 

The water flux, J, which is normally expressed as kg (or L) m h is proportional to the water vapor pressure gradient, Apm, between the feed-membrane and strip-membrane interfaces, and the membrane mass transfer co-efficient K, [Eq. (3)]. The vapor pressure gradient between the two interfaces depends on the water activity, a, in the bulk feed and strip streams, and the extent to which concentration polarization reduces that activity at each interface. Whilst can be estimated using established diffusional transport equations, it is more difficult to estimate values for the water vapor pressure at the membrane wall for use in Eq. (3). However, an overall approach using the vapor pressures of the bulk solutions and semi-empirical correlations that take account of the different conditions near the membrane wall can be used to estimate J. 

Knudsen numbers signify the coexistence of both mechanisms. Fickian diffusion is significantly slower than Knudsen diffusion at the same vapor pressure gradient. Experimental measurements of water flux in the presence and absence of air in the pores have shown a two to three-fold increase on degassing. Lowering the total gas pressure in the pores decreases the frequency of water vapor-air collisions, and thereby increases the mean free path of the water molecules. However, feed pretreatment by heating or exposure to a vacuum to remove air is often counterproductive to the preservation of product quality. 

The water flux achieved in OD can be described in terms of an overall mass transfer co-efficient, K, and the water vapor pressure gradient between the bulk feed and strip streams [Eq. (10)]. The total resistance to mass transfer, given by l/K, is the sum of three separate resistances in series [Eq. (11)]. Here, l/Kf, l/Kj and l/K are the resistances imposed by the feed-side boundary layer, the membrane, and the strip-side boundary layer respectively. 

The water vapor flux increases exponentially as the mean temperature of the system increases in accordance with the Antoine equation [Eq. (17)]. Here, T is the absolute temperature and A, B, and C are constants. Temperature also affects water flux through the thermal sensitivity of solution viscosity, solute dif-fusivity, and the diffusion co-efficient of water vapor in air-filled membrane pores. Elevated temperatures tend to lower feed-side, membrane, and strip-side resistances to mass transfer. However, operation at such temperatures may lead to a loss of product integrity through thermal degradation or volatiles loss. 

The water vapor flow flux is also proportional to pressure gradient and permeability as follows ... 

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